APPM 2360 Midterm: appm2360spring2015exam1
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On the front of your bluebook write: (1) your name, (2) your student id number, (3) recitation section, (4) your instructor"s name, and (5) a grading table. Books, class notes, cell phones, and calculators are not permitted. Problem 1: (30 points) consider the differential equation dp dt. = p (1 p ) 2p (a) (5 points) find all equilibrium solutions. (b) (20 points) find the general solution p (t). (c) (5 points) solve the ivp where p (0) = 1. Using the two stage euler-lagrange method (i. e. , method of variation of parameters) show that the particular solution has the form where v(t) satis es yp(t) = v(t)ecos t dv dt. Problem 3: (30 points) answer the following questions true or false. Problem 4: (30 points) alice is a graduate student in chemistry. In her lab she nds a tank that contains 10 gallons of chemical solution, which she labels as solution a.
